How many three-digit even numbers can be formed using the digits 1, 2, 3, 4 and 5 when repetition of digits is not allowed?

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NDA (Held On: 21 Apr 2019) Maths Previous Year paper

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Answer 1

Concept:

Arrangement of r things that can be done out of total n things. This is denoted by \({n_{{P_r}\;}}\)

\(\Rightarrow \;{n_{{P_r}\;}} = \frac{{n!}}{{\left( {n - r} \right)!}}\)

Calculation:

For even number unit digit can be filled in two ways (2 or 4 can be put on unit place)

Remaining two digits can be filled in \({\rm{}}{4_{{{\rm{P}}_2}{\rm{}}}}\)

Number of even numbers \({\rm{}} = {\rm{}}2 \times {\rm{}}{4_{{{\rm{P}}_2}{\rm{}}}}{\rm{}} = {\rm{}}2 \times 12{\rm{}} = {\rm{\;\;}}24\)